Method and apparatus for electronically evaluating the internal temperature of an electrochemical cell or battery

ABSTRACT

A testing device applies time-varying electrical excitation to a cell or battery and senses the resulting time-varying electrical response. Computation circuitry within the device uses voltage and current signals derived from the excitation and response signals as inputs and computes values of elements of an equivalent circuit representation of the cell or battery. The internal temperature of the cell or battery is calculated from the value of the time constant of a particular parallel G-C subcircuit of the equivalent circuit. The battery&#39;s internal temperature is then either displayed to the user, used to apply appropriate temperature corrections to other computed quantities, used to detect thermal runaway, and/or used to control an external process such as charging of the battery.

This is a Divisional application of U.S. patent application Ser. No.09/388,276, filed Sep. 1, 1999 now U.S. Pat. No. 6,137,269.

BACKGROUND OF THE INVENTION

The present invention relates to testing of storage batteries. Morespecifically, the invention relates to measuring temperature of anelectrochemical cell or battery.

When testing or evaluating the performance of cells and batteries, it isdesirable to accurately know battery temperature in order to applyappropriate temperature corrections to the measured results. For exampleChamplin, in U.S. Pat. No. 3,909,708, describes setting a dial on thetester to the battery's temperature in order to cause the measureddynamic conductance to comport with that of a battery at roomtemperature. However, exactly how this battery temperature informationis to be obtained is not discussed. Others employ a very roughcorrection by instructing the user to push a button when the ambienttemperature is, e.g., “below 0° C. ”. Marino et al., in U.S. Pat. No.4,423,378 refer to a battery temperature “probe” whose output isinputted to a microprocessor for the purpose of correcting load-testresults. Similar temperature probes are described by Alber et al. inU.S. Pat. No. 4,707,795. Other workers have attached thermistors to testclips so that they would be in thermal contact with a battery terminal,or have placed them in thermal contact with the battery's case. Eveninfrared techniques have been used to determine battery casetemperature.

All of these prior art techniques have measured either the battery'sambient temperature or its external case temperature. Unfortunatelyhowever, these quantities can be very different from the actual internaltemperature of the battery—the truly desired quantity. These temperaturedifferences come about from localized internal heating caused bycurrents flowing through the battery, from the large thermal mass of thebattery, and from the poor thermal contact between the battery and itsenvironment. For example, an automobile engine compartment will warm uprapidly with the engine running. If the battery is cold, however, itsinternal temperature will remain low for a very long period of time.

SUMMARY OF THE INVENTION

A testing device applies time-varying electrical excitation to a cell orbattery and senses the resulting time-varying electrical response.Computation circuitry within the device uses voltage and current signalsderived from the excitation and response signals as inputs and computesvalues of elements of an equivalent circuit representation of the cellor battery. The internal temperature of the cell or battery iscalculated from the value of the time constant of a particular parallelG-C subcircuit of the equivalent circuit. In various aspects, thebattery's internal temperature is then displayed to the user, used toapply appropriate temperature corrections to other computed quantities,used to detect thermal runaway, and/or used to control an externalprocess such as charging of the battery.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a device for measuring the internaltemperature of an electrochemical cell or battery according to thepresent invention.

FIG. 2 depicts a six-element small signal equivalent circuitrepresentation of a particular automotive storage battery.

FIG. 3 is a plot of the variation of the three subcircuit time-constantsdefined in FIG. 2 as functions of the charge removed from the battery.

FIG. 4 is a plot of measured and theoretical values of time constant τ₃defined in FIG. 2 as functions of the internal temperature of thebattery.

FIG. 5 is a plot of the inverse of the relationship plotted in FIG. 4.

FIG. 6 is a circuit representation of the parallel G3-C3 subcircuitshowing its admittance Y3.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Clearly, a method and apparatus for electronically determining the trueinternal temperature of a cell/battery would be of great value. Thepresent invention addresses this need.

A very important application of the method taught herein is in thedetection of “thermal runaway”—a phenomenon in which the internaltemperature of a battery undergoing charging rises catastrophically(see, e.g., McShane et al., U.S. Pat. No. 5,574,355). Using thetechnique disclosed below, a runaway condition can be quickly detectedby a precipitous internal temperature rise, which, in turn could be usedto shut off the charger or reduce its charging voltage.

FIG. 1 discloses a block diagram of apparatus for evaluating a battery'sinternal temperature according to the present invention. Apparatus ofthis type is fully disclosed in pending U.S. patent application Ser. No.09/152,219, filed Sep. 11, 1998 and entitled “METHOD AND APPARATUS FORMEASURING COMPLEX IMPEDANCE OF CELLS AND BATTERIES” and pending U.S.patent application Ser. No. 09/151,324, filed Sep. 11, 1998, entitled“METHOD AND APPARATUS FOR DETERMINING BATTERY PROPERTIES FROM COMPLEXIMPEDANCE ADMITTANCE” which are incorporated herein by reference.Measuring circuitry 10 electrically couples to cell/battery 20 by meansof current-carrying contacts A and B and voltage-sensing contacts C andD. Measuring circuitry 10 passes a periodic time-varying current i(t)through contacts A and B and senses a periodic time-varying voltage v(t)across contacts C and D. By appropriately processing and combining i(t)and v(t), measuring circuitry 10 determines real and imaginary parts ofa complex parameter, either impedance Z or admittance Y, at a measuringfrequency f_(k); where f_(k) is a discrete frequency contained in theperiodic waveforms of both i(t) and v(t).

Control circuitry 30 couples to measuring circuitry 10 via command path40 and commands measuring circuitry 10 to determine the complexparameter of cell/battery 20 at, each one of n discrete measuringfrequencies, where n is an integer number. This action defines 3nexperimental quantities: the values of the n measuring frequencies andthe values of the n imaginary parts and n real parts of the complexparameter at the n measuring frequencies.

Computation circuitry 50 couples to measuring circuitry 10 and tocontrol circuitry 30 via data paths 60 and 70, respectively, and acceptsthe 2n experimental values from measuring circuitry 10 and the values ofthe n measuring frequencies from control circuitry 30. Upon a “BeginComputation” command from control circuitry 30 via command path 80,computation circuitry 50 uses algorithms disclosed in U.S. patentapplication Ser. No. 09/151,324 to combine these 3n quantitiesnumerically to evaluate 2n elements of an equivalent circuitrepresentation of the cell/battery. Computation circuitry 50 thencalculates the internal temperature of the cell/battery from values ofparticular elements of this circuit representation. Finally, computationcircuitry 50 outputs the computed result to the user on display 90and/or uses the result to activate an alarm 100 or to control a process110 such as a battery charger.

In practice, a microprocessor or microcontroller running an appropriatesoftware program can perform the functions of both control circuitry 30and computation circuitry 50.

FIG. 2 discloses a six-element equivalent circuit representation of atypical automotive storage battery. This circuit representation wasevaluated using apparatus of the type disclosed in FIG. 1 with n=3 byemploying algorithms disclosed in U.S. patent application Ser. No.09/151,324. The three measurement frequencies were 5 Hz, 70 Hz, and 1000Hz. One notes that the n=3 equivalent circuit comprises threesubcircuits:

A series G1-L1 subcircuit.

A parallel G2-C2 subcircuit.

A parallel G3-C3 subcircuit.

One notes further that the three subcircuits are characterized by havingvery different time constants. The shortest time constant, τ₁=L1·G1=93.5μS, belongs to the series G1-L1 subcircuit. The next longest timeconstant, τ₂=C2/G2=2.22 mS, belongs to the parallel G2-C2 subcircuit;and the longest time-constant, τ₃=C3/G3=41.6 mS, belongs to the parallelG3-C3 subcircuit. Accordingly, the three subcircuits represent quitedifferent physical processes and can be differentiated from one anotherby their time constants.

FIG. 3 is a logarithmic plot of the three time constants defined aboveas functions of charge (ampere-hours) removed from the battery. Onenotes that the three time constants remain widely separated as charge isremoved, and that the longest of the three, τ₃, is nearly independent ofstate-of-charge. This result is important to the present invention.

FIG. 4 discloses the observed variation of time constant τ₃=C3/G3 withinternal battery temperature. One sees that τ₃ varies inversely withtemperature. This variation is consistent with a theoretical model thatassociates the G3-C3 subcircuit with a linearized, small-signal,representation of the nonlinear electrochemical reaction occurring atthe negative plates. For such a model, the RC product τ₃=C3/G3represents the reaction time for the process and therefore variesinversely with temperature. By empirically establishing thisrelationship between τ₃ and T, one can actually utilize measurements ofτ₃ to determine the battery's internal temperature, T.

FIG. 4 shows experimental points compared with a theoretical τ₃(T_(c))relationship. Note that the steepest slope, and hence the most accuratetemperature determination, occurs in the most interesting region between−20° C. and +20° C. The theoretical curve disclosed in FIG. 4 is a plotof the following equation: $\begin{matrix}{{\tau_{3}( T_{c} )} = {K_{3} + \frac{1}{\frac{1}{K_{2}} + \frac{1}{K_{1}\exp \quad \{ {{qV}_{0}/{k( {T_{c} + {273{^\circ}}} )}} \}}}}} & (1)\end{matrix}$

where τ₃ is the time constant measured in milliseconds and T_(c) is theinternal temperature measured in degrees Celsius. Physical parametersintroduced in this equation are:

k=1.38×10⁻²³ Joules/° K (Boltzman's Constant)

q=1.6×10⁻¹⁹ Coulombs (electronic charge)

V₀=0.85 eV (activation energy)

The three constants K₁, K₂, and K₃ were empirically determined to be

K₁=2.0×10⁻¹⁴

K₂=67.0 mS

K₃=37.0 mS

One notes excellent agreement between theory and experiment.Measurements show that τ₃ is virtually independent of battery size andstate-of-charge (see FIG. 3). Thus, this empirical τ₃(T_(c))relationship plotted in FIG. 4 appears to be quite universal.

In order to determine internal temperature from time constantmeasurements, one must mathematically invert the above τ₃(T_(c))relationship to obtain a T_(c)(τ₃) relationship. The result is:$\begin{matrix}{{T_{c}( \tau_{3} )} = {\frac{( {{qV}_{0}/k} )}{\ln \quad \{ \frac{( {K_{2}/K_{1}} )( {\tau_{3} - K_{3}} )}{( {K_{2} + K_{3} - \tau_{3}} )} \}} - {273{^\circ}}}} & (2)\end{matrix}$

where the parameters and constants, q, V₀, k, K₁, K₂, K₃, are the sameas those introduced in the τ₃(T_(c)) relationship.

The inverse theoretical T_(c)(τ₃) curve is plotted in FIG. 5. Byemploying this relationship, one can readily determine the battery'strue internal temperature from measurements of τ₃. This importanttemperature information can then be used to apply accurate temperaturecorrections to other measured quantities, such as CCA, state-of-charge,and amp-hour capacity. It can also be used to detect a thermal runawaycondition, and to control an external process such as a battery charger.

This completes the disclosure of my invention. FIG. 6, however, willplace the true nature of the invention in greater perspective. FIG. 6illustrates the G3-C3 subcircuit and shows that the complex admittanceof this parallel subcircuit, Y3=G3+jωC3, explicitly contains the twoquantities, G3 and C3, necessary to determine the battery's internaltemperature. Thus, my discussion above actually discloses a relationshipexisting between the real and imaginary parts of Y3 and the internaltemperature of the battery. Although it is true that complex Z andcomplex Y are reciprocals of one another, no simple relationship existsbetween the real and imaginary parts of impedance Z3 and time constantτ₃. Accordingly, the results of any ac measurement must be expressed incomplex admittance form—not complex impedance form—in order to observethe important relationship that I have disclosed herein. How thiscomplex admittance is obtained, however, is relatively unimportant.

Although my disclosure has relied upon particular apparatus andalgorithms previously disclosed in U.S. patent applications Ser. No.09/152,219 and Ser. No. 09/151,324, other methods will be apparent toone skilled in the arts. For example, one can employ bridges or othertypes of apparatus to measure complex admittance (or its reciprocal,complex impedance). Furthermore, if accuracy is not a strictrequirement, one can take advantage of the fact that the various timeconstants are widely separated from one another and simply assume thatthe subcircuits are not coupled. Within this approximation, C2 and C3are treated as short circuits at frequencies near f₀₁=½ πτ₂, L1 and C3are treated as short circuits at frequencies near f₀₂=½ πτ₁, and atfrequencies near f₀₃=½ πτ₃, L1 is treated as a short circuit while C2 istreated as an open circuit. Thus, with some batteries, it is possible toobtain satisfactory results from a very simple analysis of measurementsat two or three frequencies. With certain batteries, it is even possibleto obtain useful approximations to Y3 from measurements of complex Y orZ=1/Y obtained at a single, appropriately chosen, frequency. Workersskilled in the art will recognize that these and other variations may bemade in form, and detail without departing from the true spirit andscope of my invention.

What is claimed is:
 1. Apparatus for determining the internaltemperature of an electrochemical cell or battery comprising: electricalexcitation circuitry adapted to apply multiple frequency electricalexcitation to said cell or battery; electrical response sensingcircuitry configured to sense an electrical response of said cell orbattery to said multiple frequency electrical excitation; andcomputation circuitry responsive to said multiple frequency electricalexcitation and to said electrical response and adapted to evaluate saidinternal temperature from computations performed in accordance with saidmultiple frequency electrical excitation and said electrical response.2. The apparatus of claim 1 including a display device coupled to saidcomputation circuitry for conveying a computed value of said internaltemperature to a user.
 3. The apparatus of claim 1 wherein saidcomputation circuitry couples to an external process device and saidexternal process device is controlled by said computation circuitry inaccordance with a computed value of said internal temperature.
 4. Theapparatus of claim 1 used to detect a thermal runaway condition, saidcondition characterized by a rapid rise in said internal temperaturewhile charging said electrochemical cell or battery.
 5. The apparatus ofclaim 4 including an alarm coupled to said computation circuitry foralerting a user to said thermal runaway condition.
 6. The apparatus ofclaim 3 wherein said external process device is a battery charger. 7.Apparatus as in claim 1 wherein said multiple frequency electricalexcitation is multiple frequency electrical current excitation and saidelectrical response is electrical voltage response.
 8. The apparatus ofclaim 1 wherein said computation circuitry is further adapted toimplement a temperature correction of a measured result in accordancewith said internal temperature.
 9. The apparatus of claim 8 wherein saidmeasured result is measured dynamic conductance.
 10. The apparatus ofclaim 8 wherein said measured result is a load-test result.
 11. Theapparatus of claim 8 wherein said measured result is expressed as CCA.12. The apparatus of claim 8 wherein said measured result is expressedas state-of-charge.
 13. The apparatus of claim 8 wherein said measuredresult is expressed as amp-hour capacity.
 14. A method forelectronically evaluating the internal temperature of an electrochemicalcell or battery comprising the steps of: applying multiple frequencyelectrical excitation to said cell or battery; sensing an electricalresponse to said multiple frequency electrical excitation; combiningvalues of said multiple frequency electrical excitation and saidelectrical response mathematically to obtain a computed result; andevaluating said internal temperature from said computed result.
 15. Themethod of claim 14 including the additional step of displaying saidinternal temperature to a user.
 16. The method of claim 14 including theadditional step of controlling an external process device in accordancewith said internal temperature.
 17. The method of claim 14 wherein saidmultiple frequency electrical excitation is multiple frequencyelectrical current excitation and said electrical response is electricalvoltage response.
 18. The method of claim 14 including the additionalstep of implementing a temperature correction of a measured quantity inaccordance with said internal temperature.
 19. The method of claim 18wherein said measured quantity is dynamic conductance.
 20. The method ofclaim 18 wherein said measured quantity is a load-test quantity.
 21. Themethod of claim 18 wherein said measured quantity is expressed as CCA.22. The method of claim 18 wherein said measured quantity is expressedas state-of-charge.
 23. The method of claim 18 wherein said measuredquantity is expressed as amp-hour capacity.
 24. A method forimplementing a temperature correction of a measured property of anelectrochemical cell or battery comprising the steps of: applyingmultiple frequency electrical excitation to said cell or battery;sensing an electrical response to said multiple frequency electricalexcitation; combining values of said multiple frequency electricalexcitation and said electrical response mathematically to compute atemperature correction factor; and adjusting the value of said measuredproperty in accordance with said computed temperature correction factor.25. The method of claim 24 wherein said measured property is measureddynamic conductance.
 26. The method of claim 24 wherein said measuredproperty is a measured load-test property.
 27. The method of claim 24wherein said measured property is expressed as CCA.
 28. The method ofclaim 24 wherein said measured property is expressed as state-of-charge.29. The method of claim 24 wherein said measured property is expressedas amp-hour capacity.
 30. The method of claim 24 wherein said multiplefrequency electrical excitation is multiple frequency electrical currentexcitation and said electrical response is electrical voltage response.31. A method for detecting thermal runaway of an electrochemical cell orbattery undergoing charging comprising the steps of: applying multiplefrequency electrical excitation to said cell or battery; sensing anelectrical response to said multiple frequency electrical excitation;determining the internal temperature of said cell or battery from valuesof said multiple frequency electrical excitation and said electricalresponse; and responding to an abnormal increase in said internaltemperature between successive internal temperature determinations. 32.The method of claim 31 wherein said step of responding includesactivating an alarm signifying the detection of thermal runaway.
 33. Themethod of claim 31 wherein said step of responding includes changing theoutput level of a battery charger.
 34. The method of claim 31 whereinsaid multiple frequency electrical excitation is multiple frequencyelectrical current excitation and said electrical response is electricalvoltage response.
 35. Apparatus for electronically evaluating theinternal temperature of an electrochemical cell or battery adapted forperforming the steps according to claim
 14. 36. Apparatus forimplementing a temperature correction of a measured property of anelectrochemical cell or battery adapted for performing the stepsaccording to claim
 24. 37. Apparatus for detecting thermal runaway of anelectrochemical cell or battery undergoing charging adapted forperforming the steps according to claim 31.